Distribution of cage size smooths the transition from diffusive to caging in microrheology

A colloidal particle undergoing Brownian motion and interacting with macromolecular structures embedded in complex fluids usually presents a diffusion regime at short times, with a diffusion coefficient related to the viscosity of the host solvent, and an intermediate regime where the mean squared displacement is found to be almost constant. This effect is attributed to the particle confinement in a cage formed by the surrounding complex fluid that hinders the motion of the tracer particle. An anomalous smooth transition that may span several decades usually characterises such a short-to-intermediate transition. In this work, this transition was studied using 1D, 2D, and 3D random walker simulations, finding that the origin of the smooth transition is a wide distribution of confining cages and the corresponding ensemble-averaged 3D mean squared displacement over all confined particles. The wider the cage distribution, the smoother the transition. Our results give the physical origin of the smooth transition, usually only discussed in terms of a distribution of relaxation times. [GRAPHICAL ABSTRACT]